/sci/ - Science & Math

Young deligne is a cute

>>10417077
>what is f(x) + epsilon

What textbooks should I read to understamd the theory behind the mandelbrot set and fractals? I know they have things called limit points and a hundred oeis entries, what field are they studied in?

>>10418548
>riemann integrable implies continuous

>>10418548
Constructive proofs suck, but you gotta do what you gotta do.

>>10417432
Quick question. I was reading about stokes theorem on piskunov's calculus and he often uses a cosine with 2 arguments, something like this [math] \cos{(n, x)} [/math] what the hell does that mean? He doesn't say anywhere wtf that is.

>>10418577
This is a wild guess but maybe you interpret it as coordinate positions, like cos(n, x) = cos(n), cos(x)? That sounds dumb but maybe

>>10418620
Is supposed to be a unit normal vector, idk if that helps

>>10418638
N is supposed to be a unit normal vector

>>10418564
am retarded, thought g(x) merely had to be RI.
actual solution is to construct g(x) such that any point discontinuities in f(x) are removed and any jump discontinuities are interpolated by lines of arbitrarily large slope.

>>10418577
Does he mean cos^n(x)?

all right guys my friend and I need halp. We are in multivariable calc, and we are having issues with green's theorem and potential functions. Any help on explaining the key concept behind this stuff would be greatly appreciated

>>10418836
they're literally obvious
greens theorem is literally "swirly inside equals swirly outside" or "fwoosh out = fwoosh inside"
potential functions could not be more trivial

just spent an hour on a theorem only to realize I was missing one stupid little trivial detail to piece it all together... ;-;

>>10418836
>the key concept behind
The key concept behind is that differentiation and integration are somehow "dual" to each other. This is due to the singular comology groups being isomorphic to de Rham cohomology. Just like in the fundamental theorem of calculus where, instead of integrating a derivative over an interval you could just calculate the function and endpoints, here, instead of calculating a special "derivative" of a vector field over a region you can just calculate the vector field itself over the boundary.
The best intuitive explanation is to work through the proof yourself (perhaps omitting technicalities like differentiability).

>>10418980
> and endpoints
*at

>29yo next month
>no theorem is named after me
Is it time to kys myself?

>>10419471
yep
better luck next life

>>10419471
No, you can be fine until 30 as long as some other concept is named after you

>>10418809
>partition [a, b]
>make a function that linearly connects f(a) to f(x_1), f(x_1) to f(x_2), etc
>apply Darboux

Taking a course on mathematical logic and I don't know how to prove this. Anyone decent with model theory?

>>10419549
Stop writing with a meme pen

>>10419578
Tell that to the professor.

>>10418577
Russian here, it is obviously the cosine of the angle between your vector x and a unit normal vector n.

I have mathematical proof why I personally cannot build muscle

>>10419622
Considering >>10418638 , seconded.

>>10419624
>tfw have to compute TREE(3) in order to build muscle

>>10417432
Is morphism surjective?
Why can’t wiki writer put this simple information?

>not inventing new algebraic structures
Brainlets

>>10419744
answer this
>>10419722

What happens when you take the curl of a curl? i dont understand whats happening when I do this with Maxwell's equations

>>10419739
>Is morphism surjective?
not necessarily

>Why can’t wiki writer put this simple information?
surely you should be able to show the existence of the trivial morphism just from the definition
(G,*) and (H,~) groups
f : G -> H
f(a*b)=f(a)~f(b)
f(x) = e For all x, where e is the identity in H is a valid morphism and isnt surjective

>>10419777
Why do your group have different operator?
I am learning

>>10419786
its done for more generality
if a morphism is specifically between a group and itself then its called an automorphism

>>10419786
What did he mean by this?

>>10419786
Sometimes people write every group's operator as just * (or +) but this is an abuse of notation since the operators usually mean different things and work on different sets.
To explain it unambiguously, anon was just using different notation for the two operators so that it is clear what he means.

>>10419824
*endomorphism

>>10419786

>>10417432
Guya, I'm following the /sci/ Wiki and have done a normal undergrad physics education, but i want to start from Kisilev's geometry?

Where can I find solutions for this: Kiselev's Geometry: Book I. Planimetry

>>10419973
shit i knew it was wrong but i couldnt remember the right term

>>10418836
read this
http://www.math.ucla.edu/~josephbreen/Green_s_Theorem.pdf

What does [math]S^3\{ 2^{n+1} \}[/math] mean? What are they doing to the 3-sphere?

>>10420053
www.b-ok.cc

I have a question on statistics.
I'm scraping data from acceptation scores of university qualification exams.
Beside tons of missing data, there's a point I'm not so sure about.
I have for several uni: how many applied, how many got rejected in the first round and how many entered the uni.

The problem is: the same student can apply for several uni but only enter one (or none).
How can I handle this?
This is not quite like survival data.
I don't have access to individual student data. Just statistics per uni.

>>10420262
Get more data or bust. If you're using data for every uni in your country, you can use (very likely) already available data on the number of people who applied to uni, and then estimate the overlap based on overall uni evaluations.

>>10420312
There's quite a lot of data. I'm still scraping. http://www.scei-concours.fr/statistiques.php
Data is also redundant. (acceptance ratio by uni AND acceptance ratio by school before uni).
But as I say, the modeling is challenging.
>Top tier uni
Very low "acceptance rate" -> I can assume the selection is very discriminating
> Low tier uni
Lots of people apply just in case but got accepted in a better uni. So overall, the acceptance ratio is low because there's few people getting in compared to the number of people who applied.

>>10419549
First question: the language L does not contain the constant symbol 'c', and so it happens for your sentence. Hence the interpretation of the formula is the same.

Second question, For delta just use the first point. Followig the hint:
. Assume that M satisfies phi(a) for some a in M; then you interpret the costant symbol 'c' as 'a', and so M_c satisfies L_c.
. Assume that this is not true; then you can interpret 'c' as anything (say again 'a' in M). In fact, for any b in M, you have that phi(b) is false, phi^c is false, so phi(b) -> phi^c is true and M_c satisfies L_c.

They are quite disappointing as exercises.

>>10420219
>Kiselev's Geometry: Book I. Planimetry
I don't see this book here anon :(

Are you sure the solutions for it are there?

Could someone please tell me what the FUCK this picture is? It's always used for the p-adic integers but I have no idea what it's actually showing.

>>10420747
https://math.stackexchange.com/questions/583609/p-adic-numbers-and-group-characters
Same question here

>>10420736
https://b-ok.cc/s/?q=Kiselev%27s+Geometry%3A+Book+I.+Planimetry+
Nigger

What's this property called?
It doesn't seem to be homotopy equivalence directly, since homotopy equivalence just demands one function g for the f. Pic related however is a weaker property, where you need g and h that don't have to be the same.
Also, in the latter case, how do I show that the property is even reflective?

>>10419622
Kek, "obviously".

>>10419624
Go read /fit/s sticky

>T. /fit/ bro

retaking calc 3 because I got a C. how much of a brainlet am I?

no one told me it was going to be a fucking art class

>>10420947

>>10420788
I'M ASKING FOR SOLUTIONS TO THE PROBLEMS IN THERE ANON

aka

the ANSWER key

pls no bully

Any decent audiobooks for topology and differential equations?

>>10421247
I don't think an official solution key exists, but people do type up their answers
https://github.com/docs-santanu/kiselev-geometry-1
this may help.

>>10418560
I'm also curious about this

FUCK grad school

>>10421976
Why?

>Thm 1.10 - Probabilistic Version - Part 04 - Trivial Relation Between Q-Pilot and Theta-Pilot
https://www.youtube.com/watch?v=yZZfvxBnBus

>Thm 1.10 - Probabilistic Version - part 05 - Ramification Term, "Extra Term"
https://www.youtube.com/watch?v=aUQqnITi5xo

learning about Riesz representation theorem tomorrow. can I get a quick rundown?

>>10422327
every linear functional in hilbert space is an inner product
usually most functionals are much more complicated than simple inner product maps but hilbert space is extremely nice

Are the p-adics useful for anything else or did someone just get high and dream up an alternative metric on Q? Also, what are some interesting results on the p-adics?

>>10422327
Consider a vector in an infinite dimensional space. As you've learned in Linear Algebra 1, we can write it out as a collumn vector according to a basis.
As you should have learned, we can similarly write linear functionals as horizontal vectors and doing matrix multiplication from the left. Verifying it works is easy, we write out a basis for the dual, and write the linear functional as a linear combination.
This gives a bijection between (collumn) vectors and linear functionals (row vectors) the obvious way: we spin it ninety degrees.
You likely also noticed that multiplying a row vector by a collumn vector with the row vector on the left is really similar to taking the dot product. What all of this means is that, for finite vector spaces, we can take a linear functional, spin it, and take dot products from the left to evaluate it.

Riesz's representation theorem says all of this still works in infinite dimensional Hilbert spaces. You'll see a couple more results like this later.

>You'll see a couple more results like this later.
like a bomb in your mail rapcak

>get e-mail from graduate school this morning
>hello sorry we forgot to put an expiry date on your acceptance letter
>btw it expires tomorrow xD

Good book for topology having learned a bit of analysis?

>>10417432
anyone knows a book focusing on factoring?
i have a hard time following book examples and turns out im shit at factoring

>>10423359
what do you mean factoring? like pre-calculus shit?

>>10423362
https://www.mathsisfun.com/algebra/factoring.html
sometimes the book throws a trigonometric identity in the demonstration and i just get lost. e.g. to find the derivative of sin(x) or cos(x).

>>10423362
[eqn]
\frac{d\sin{(x)}}{dx} = \lim_{h\rightarrow 0}\frac{\sin{(x + h)} - \sin{(h)}}{h} \\
= \lim_{h\rightarrow 0}\frac{\sin{(x)}\cos{(h)} + \cos{(x)}\sin{(h)} - \sin{(h)}}{h} \\
= \lim_{h\rightarrow 0}\frac{\sin{(x)}(\cos{(h)} - 1) + \cos{(x)}\sin{(h)}}{h} \\
= \lim_{h\rightarrow 0}\left[\sin{(x)}\frac{(\cos{(h)} - 1)}{h} + \cos{(x)}\frac{\sin{(h)}}{h}\right] \\
= \lim_{h\rightarrow 0}\sin{(x)}\lim_{h\rightarrow 0}\frac{(\cos{(h)} - 1)}{h} + \lim_{h\rightarrow 0}\cos{(x)}\lim_{h\rightarrow 0}\frac{\sin{(h)}}{h} \\
= \sin{(x)} \cdot 0 + \cos{(x)} \cdot 1 = \cos{(x)}
[/eqn]

What's your favorite textbook for a lower level discrete math course? We're using the Gossett book in mine and I am not very fond of it, I'd like to find a different one to practice with.

>>10423491
Just get a proofs book like Book of Proof

>>10423491

>>10423530
>>10423532
Ok, thanks for the recommendations. Grabbed the book of proof pdf, will try hunting down some of the others later.

>>10423433
[math] \displaystyle \lim_{h \rightarrow 0}{\frac{cos(h)-1}{h}} = 0 [/math]
are you gonna bother with showing this one?

>>10423734
The cosine function is continuous.

>>10423734
i am a brainlet anon, i just posted that to show the kind of stuff that makes me stumble.
but here https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-new/ab-1-8/v/1-cosx-over-x-as-x-approaches-0?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB

>>10418560
>what field are they studied in?
The complex plane, duh.

>>10423742
>complex plane
>field
yikes

>>10423744
the complex numbers are a field

>>10423737
yeah?

>>10423740
i mean, its just keeping track of what you have in front of you
there isnt a trick to it or anything besides being familiar with the trig functions

>>10423359
One way to go about it is to do 1000s of exercises until you memorize all the identities you were taught in elementary/middle school, but that's boring, and you'd be limiting yourself to a few known cases.

If you're willing to take it a notch above, you could study polynomial factorization — this way, some classic formulae such as [math]x^3-y^3=(x-y)(x^2+xy+y^2)[/math] will make perfect sense (ever wondered why the "formula" for [math]x^3+y^3[/math] is so similar, or why the signs are the way they are?), and you'll be able to work with higher degree polynomials as well. See:

https://en.wikipedia.org/wiki/Polynomial_long_division

https://en.wikipedia.org/wiki/Ruffini%27s_rule (your best tool here, seriously)

http://poincare.matf.bg.ac.rs/~zarkom/Polynomials_EJBarbeau.pdf (especially Chapters 2 and 3)

http://faculty.bard.edu/~belk/math318/NumberTheoryPolynomials.pdf (ignore the bits about finite fields and congruences/modular arithmetic, as these are number theoretic topics)

Once you understand this you'll realize that if [math]f(x)=x^3-y^3[/math], then [math]f(x)[/math] is a polynomial of degree 3. We can verify that [math]f(y)=0[/math] — thus, [math]y[/math] is a root of [math]f(x)[/math], and by the Factor Theorem, this means that [math](x-y)[/math] divides [math]f(x)[/math]. You may then use long division or Ruffini's rule to obtain the known identity [math]f(x)=x^3-y^3=(x-y)(x^2+xy+y^2)[/math] (and verify that [math](x^2+xy+y^2)[/math] is an irreducible polynomial in [math]\mathbb{R}[x][/math], e.g. by checking the discriminant as if it were a quadratic equation). It makes sense to think about "factoring identities" this way, and it can save your ass if you forget "the formula" of whatever.

whats a good way to remember the unit circle? i can remember the coordinates, and the denominators of the angles. its the numerators i cant see a pattern for.

is there no pattern and i just need to remember? it seems like there should be a pattern. i used to remember an easy way the youtube vids dont mention, but i forgot it

>>10423808
>and the denominators of the angles. its the numerators i cant see a pattern for.
what denominators and numerators are you referring to

>>10423814
sorry i thought i posted the pic. the radians.
6, 3, 2, 3, 6, 1 is easy to remember, but the numerators are harder, with q1 being 1, q2 being -1, q3 being +1, and q4 being *2-1.
i figured out an easier way than that about a month ago but forgot it pretty quickly

>>10423826
if you go around this unit circle counterclockwise then the pattern for sin is just 0,1,2,3,4,3,2,1,0 with a square root on top

>>10423831
can you elaborate a bit more? im not seeing that pattern for sin, i can remember that though since its either 0, 1, 1/2 sqrt(3) / 2 and their negatives. and i can picture the circle and their y coords

>>10423844
for 30 degrees, sin is sqrt(1)/2 (which is 1/2)
one notch counterclockwise to 45, sin is sqrt(2)/2
another notch to 60, sin is sqrt(3)/2
at 90, sin is sqrt(4)/2 (which is just 1)
then 120 is sqrt(3)/2 again, 135 is sqrt(2)/2, 150 is 1/2, and so on

you can see that every tick moves the numerator by 1

>>10423491
None of them. Youre better of getting a well regarded introductory axiomatic set theory book and a similar book on combinatorics. Then just read the first few chapters of each (you dont really need to go very deel in either subject). The rest (e.g. graph theory, algorithms, etc.) you can pick up along the way.

>>10417432
[math]\color{#781b86}{\tt{Cr}}\color{#65319e}{\tt{yp}}\color{#5147b7}{\tt{to}}\color{#3e5dcf}{\tt{gr}}\color{#527bb3}{\tt{ap}}\color{#669996}{\tt{hy}}\color{#7ab77a}{\tt{~I}}\color{#8ab96d}{\tt{S~}}\color{#99ba60}{\tt{/s}}\color{#a9bc53}{\tt{ci}}\color{#b9b94a}{\tt{/-}}\color{#c8b144}{\tt{re}}\color{#d7aa3e}{\tt{la}}\color{#dd9037}{\tt{te}}\color{#dc642e}{\tt{d!}}\color{#db3725}{\tt{!!}}[/math]

[math]\color{#781b86}{\text{>>}}\color{#702490}{\text{10}}\color{#672e9b}{\text{42}}\color{#5f37a5}{\text{28}}\color{#5741b0}{\text{9 }}\color{#781b86} \\
{\text{>>}}\color{#702490}{\text{10}}\color{#672e9b}{\text{42}}\color{#5f37a5}{\text{36}}\color{#5741b0}{\text{9 }} \\
\color{#781b86}{\text{Th}}\color{#702490}{\text{er}}\color{#672e9b}{\text{e'}}\color{#5f37a5}{\text{s }}\color{#5741b0}{\text{a }}\color{#4f4aba}{\text{fu}}\color{#4654c5}{\text{ck}}\color{#3e5dcf}{\text{in}}\color{#476bc2}{\text{g }}\color{#5079b5}{\text{co}}\color{#5a87a8}{\text{ns}}\color{#63949b}{\text{pi}}\color{#6ca28e}{\text{ra}}\color{#75b081}{\text{cy}}\color{#7eb777}{\text{ g}}\color{#86b870}{\text{oi}}\color{#8eb96a}{\text{ng}}\color{#95ba64}{\text{ o}}\color{#9dbb5d}{\text{n }}\color{#a5bc57}{\text{wi}}\color{#adbd50}{\text{th}}\color{#b4bb4c}{\text{ t}}\color{#bbb849}{\text{hi}}\color{#c2b446}{\text{s }}\color{#c9b143}{\text{sh}}\color{#d0ad41}{\text{it}}\color{#d7aa3e}{\text{ g}}\color{#dea63b}{\text{et}}\color{#dd9337}{\text{ti}}\color{#dd8034}{\text{ng}}\color{#dc6d30}{\text{ d}}\color{#dc5a2c}{\text{el}}\color{#db4728}{\text{et}}\color{#db3425}{\text{ed}}\color{#da2121}{\text{.}}[/math]

>>10423873
>>10423881
[math]\color{#781b86}{\text{ne}}\color{#6f2591}{\text{ma}}\color{#662f9c}{\text{to}}\color{#5d39a8}{\text{de}}\color{#5444b3}{\text{ m}}\color{#4b4ebe}{\text{od}}\color{#4258c9}{\text{s }}\color{#4263c9}{\text{ai}}\color{#4b70bd}{\text{n'}}\color{#537db1}{\text{t }}\color{#5c8aa4}{\text{sm}}\color{#659798}{\text{ar}}\color{#6da48c}{\text{t }}\color{#76b180}{\text{en}}\color{#7eb777}{\text{ou}}\color{#87b870}{\text{gh}}\color{#8fb969}{\text{ f}}\color{#98ba62}{\text{or}}\color{#a0bb5b}{\text{ /}}\color{#a9bc54}{\text{mg}}\color{#b1bd4d}{\text{/ }}\color{#b7ba4a}{\text{so}}\color{#beb648}{\text{ I}}\color{#c4b345}{\text{'m}}\color{#cbb043}{\text{ p}}\color{#d1ad40}{\text{ut}}\color{#d8a93e}{\text{ti}}\color{#dea63b}{\text{ng}}\color{#dd9237}{\text{ t}}\color{#dd7d33}{\text{hi}}\color{#dc692f}{\text{s }}\color{#dc542b}{\text{he}}\color{#db4027}{\text{re}}\color{#da2b23}{\text{. }} \\
\color{#781b86}{\text{Fo}}\color{#6f2591}{\text{rm}}\color{#662f9c}{\text{at}}\color{#5d39a8}{\text{ti}}\color{#5444b3}{\text{ng}}\color{#4b4ebe}{\text{ i}}\color{#4258c9}{\text{n }}\color{#4263c9}{\text{ra}}\color{#4b70bd}{\text{in}}\color{#537db1}{\text{bo}}\color{#5c8aa4}{\text{wT}}\color{#659798}{\text{eX}}\color{#6da48c}{\text{ a}}\color{#76b180}{\text{s }}\color{#7eb777}{\text{a }}\color{#87b870}{\text{fi}}\color{#8fb969}{\text{na}}\color{#98ba62}{\text{l }}\color{#a0bb5b}{\text{co}}\color{#a9bc54}{\text{un}}\color{#b1bd4d}{\text{te}}\color{#b7ba4a}{\text{rm}}\color{#beb648}{\text{ea}}\color{#c4b345}{\text{su}}\color{#cbb043}{\text{re}}[/math]

>>10423888
Based schizoposter

>>10423888
???

>>10423808
You can derive them using Pythagoras' theorem. Square for π/4, equilateral triangle for π/6 and π/3.

sin(π/4)=cos(π/4), sin^2+cos^2=1 => 2sin^2(π/4))=1 => sin^2(π/4)=1/2 => sin(π/4)=1/sqrt(2) (= sqrt(2)/2).

If you join one vertex of an equilateral triangle to the midpoint of the opposite edge, you get sin(π/6)=(l/2)/l = 1/2. sin^2+cos^2=1 => 1/4+cos^2(π/6)=1 => cos^2(π/6)=3/4 => cos(π/6)=sqrt(3)/2.

By reflection in y=x, sin(π/3)=cos(π/6), cos(π/3)=sin(π/6).

>the book makes sure to specify that the ring is associative
What the fuck even is the definition of ring at this point, abelian associative operation, distributive operation and non-empty?

Post readings and doings

>>10424463
There is a point. For example, the octonions are not associative, but they are a perfectly good algebraic object. They even have a well defined division, so they're a division ring without associativity

>>10423888
I'm on mobile. What is the TeX saying?

>>10424493
What's that book holder?
Can you please send a picture of the entire table?

>>10424827
s-sure

>>10423532
This is the worst list ive seen

>>10425177
Very cool!

>>10425177
every copy of this book on libgen is too faded to read
this is so sad

>wrote "you" in a paper instead "we"
It's been fun lads, but I gotta kill myself now

does she exist?

>>10425509
There's a husband / wife alg. topologist couple at my uni

>>10422937
pro tip: "column" only has one "l"

>>10425518
"A hole is a hole"

What does it mean to be an anti-isomorphism in the context of functionals?

>>10423433
u fucked up

>>10425542
The functionals are isomorphic to each other's opposite

>>10425590
huh?

>>10425528
My bad, I always mix up repeating letters in english.
>>10425542
f(x+y)=f(x)+f(y)
f(xy)=f(y)f(x)
Where juxtaposition is composition.

>>10425607
>functionals
My bad once again, I read linear transformation. No idea what a functional anti-isomorphism is.

>>10425611
>This theorem establishes an important connection between a Hilbert space and its continuous dual space. If the underlying field is the real numbers, the two are isometrically isomorphic; if the underlying field is the complex numbers, the two are isometrically anti-isomorphic.
From wiki on Riesz rep theorem

>>10425618
>Riesz rep theorem
In this context it means that if we the homomorphism between the space and its dual is phi we have phi(ax) = a*phi(x) where a* is the complex conjugate of a

>>10425626
Ah, I see.

>>10425618
It's not a functional anti-isomorphism, it's an anti-isomorphism as vector spaces.
Above anon has specified the difference.

>>10425634
yeah, I should've formed my question less sloppily.

>>10425631
Note that this simply follows from an inner product being conjugate-linear in the second argument

>>10424497
That's a division algebra.

>>10424463
Ring means an associative unital Z-algebra.

what's the Rudin of abstract algebra?

>>10425688
lang <-> papa rudin
there isn't really an abstract algebra baby rudin. all the serious intro to algebra books are decent.

>>10425509
Inter-department marriages are not uncommon. I can think of at least 4-5 couples like that off the top of my head.
I know a few other people who are married to mathematicians at different universities too. No idea how they keep a marriage together living 4 or 5 hours apart.

>>10425673
That's a pretty weak joke. Couldn't you do a bit better? And would it be too much of a hassle not to tack on bait into the joke?
>>10425694
Rudin is an undergraduate text. Lang is meant for Masters courses. Absolutely no comparison.
The only thing I can come up with is someone, for some incomprehensible reason, writing up a category theory heavy book on undergrad group theory.

>>10425716
I hope for your sake you're baiting and not actually this stupid

>>10423888
Can somebody please explain this to me? What am I looking at here?

>>10425731
mental illness

>>10425775
Did Tooker get internet access in prison or something?

>>10425404
To be fair, the book printing quality is not great. It's hard to see what I mean from the pic, but the ink feels somewhat faint

>>10425780
there's no way tooker knows how to rainbowflex

buhat hi koi chuteya banda hai yeh

>>10425844
thats a shame, but its still way too advanced for me so it wont bother me for awhile

>>10425363
Yeah, it's missing the personal grooming meme

>>10425844
Looks like someone might be able to scan it decently if they cared to adjust the brightness etc. properly.
>>10425509
My ex.

>>10425509
>she

>>10418548
f=g

>>10425688
Fraleigh

>>10425890
Chup lavde

>>10426300
epic
>>10425688
probably dummit and foote

>Learns vector calculus to measure volume of anime tiddies

What's your math story, anons?

>>10418980
Not him but I asked my teacher to confirm my attempt of a proof of greens theorem during some final review session and she seized up and basically told me that was a question she wasn't ready for atm. Wtf.

Arnold - Ordinary Differential Equations
Arnold - Mathematical Methods of Classical Mechanics

Why does these get recommended so much on stackexchange? Am I missing something? They seem like meme books

>>10426632
ask rapcak he frequents this /mg/ 24/7 with his yukari tags
he will also make dumb statements or ask obvious questions like the retard he is to display his brilliance

>>10426608
I don't really have anything better to do and don't want to get an internship.
>>10426853
What.

How do you study and practice calc and trig stuff? I took a year off school and i'm in calc 1 having a fucked time remembering most things.

>>10426879
>get book with examples & solutions
>read example problem statement
>cover the solution with a paper
>try to solve it
>check your work by looking at the solution
There's no fucking mystery, just get off 4channel and do it

>>10425509
I'm so close, yet so far...

In classe we learnt the dot product over real matrices of size n: [math]\langle \mathbf {A} ,\mathbf {B} \rangle=\mathrm {tr} \left({{\mathbf {A} ^{T}}}\mathbf {B} \right)=\sum _{i,j}{ {A_{ij}}}B_{ij}\,,[/math]
Our teacher is asking us to find a dot product over complex matrices.
Using the fact that [math]z\overline z\geq 0[/math] I came up with: [math]\mathrm {tr} \left({\overline {\mathbf {A} ^{T}}}\mathbf {B} \right)=\sum _{i,j}{\overline {A_{ij}}}B_{ij}\,,[/math] which is positive-definite but not symetrical.
Extracting the symetric part of this function I get the dot product [math]\langle \mathbf {A} ,\mathbf {B} \rangle=\frac {1}{2}\mathrm {tr} \left({\overline {\mathbf {A} ^{T}}}\mathbf {B} \right)+\frac {1}{2}\mathrm {tr} \left({\overline {\mathbf {B} ^{T}}}\mathbf {A} \right)[/math].
Is there an easier way to find a dot product over any vector space? (a dumb algorithm ?)

Why is this allowed (the exercise)

>>10427126
Yes, there's always a God given algorithm

insha'Allah brother

>>10427204
That's fucked up

>>10427126
>not symmetric
It's not supposed to be symmetric. Inner products on complex vector spaces are skew-symmetric,

what is the frontier of math today and does anyone have a good chart telling how to become a good at math, to basic up to the advanced stuff? Help me, nerds.

>>10427242
Do you know what's worse? I just noticed in the proof he uses a definition and lemma that's is much in the future, definition 5.22!

>>10425506
maybe some girl will your papers someday

>>10427204
These are the worst

>>10427204
It's the "nieghborhood".

Is /sci/ good with Ramsey combinatorics? I'm stuck and can't seem to finish my proof for this one.

The complete graph on 34 vertices, K34, is edge-colored using the colors blue, red and yellow. Show that it must contain either a blue K3, a red K3, or a yellow K4.

My unfinished attempt in a nutshell: Each vertex must send at least 11 monochromatic edges. If a vertex with 11 all blue or all red edges exists, then I have shown that the theorem must hold.

I'm now struggling to prove the case where no vertex exists such that it sends 11 edges that are either all blue or all red. I deduce that in this scenario, each vertex must send at least 13 yellow edges. I thought about playing around with the subgraph of the given K34 which contains all 34 original vertices and only the 34*13 = 442 yellow edges that I know for sure must exist within the graph; thought I might try to show that this subgraph must contain some K4. But I'm not even sure if that's true; and all other attempts to proceed from here haven't been fruitful either.

Any ideas would be much appreciated!

that feel when I realized I assumed that [math]C^\infinity[/math] functions were analytic on my test

>>10427276
Nobody?

>>10427834

What's a better use of my time to do over the summer once my (honors) analysis class is done?

The stein+shakarchi meme or the sternberg/loomis advanced calculus meme? I am not doing the rudin meme under any circumstances since I could do the exercises but I dislike the book.

>>10428017
Stein+shakarchi is not even a meme compared to how much of a meme loomis is. In my opinion.

>>10428045
>compared to how much of a meme loomis is

Thank you. How is it a meme? It seems to me like a very short treatment of 100 different topics so my impression agrees with you.

>>10419476
oh ok, i'm safe then. Couldn't even imagine being over 30 and not having a mathematical concept named after me :^)

>>10426632
Both of those are truly very special books, no book on ODEs will give you so much geometric insight. Likewise, the other book covers geometric intuition behind symplectic geometry and many concepts that are generally introduced in the most obtuse and confusing way possible (exterior forms and exterior derivative, e. g.).

Not familiar with the term "meme book", however. If you don't see any value in those two books, you are likely either at the level of excellent mathematical intuition (so you think in higher-level terms such sheaves, varieties, cohomologies), or you are not educated enough to understand them (the book on ODEs in particular is not an entry-level text).

>>10427126
reread your definition of inner product
if it says an inner product is "symmetric" it's wrong and shit

>>10428017
imagine being such a fucking trog you won't read rudin
just read stein & shakarchi, it's pretty good
>>10427986
no, this isn't your little preschool pen. no one here needs to spoonfeed you.
because i'm nice, i'll tell you to look at the fucking wiki.
there's no "frontier of math" but people are very interested in arithmetic geometry (so, properties of certain algebraic curves on certain discrete sets) and dynamical systems these days. there's also good stuff to be said about number theory.

>>10428619
>imagine being such a fucking trog you won't read rudin
Rudin is a meme.

>>10427276
>a good chart
The one that is posted literally every time the question is posed (pic related). Also check out the wiki: https://4chan-science.fandom.com/wiki/Mathematics

Why do all memelists have people doing 50 intro to proofs books and learning calculus 5 times?

Non brainlets should just do hoffman+kunze and munkres topology (up until the algebraic section) then do an analysis book and never touch brainlet calculus.

>>10428716
Why would you start off with linear algebra and topology before analysis? Most lists only start off with 1 proof book, or maybe 2 telling the reader to pick one. Often they are even listed as "optional reading". I do agree however that doing stuff like
>>10428691
where you have "a taste" is fucking retarded.

>>10428716
>complains about autism
>is autistic
What did anon mean by this?

>>10428716
They don't

>>10427276
>what is the frontier of math today and does anyone have a good chart telling how to become a good at math, to basic up to the advanced stuff?

what did he/she mean by this?
https://terrytao.wordpress.com/2019/02/19/on-the-universality-of-the-incompressible-euler-equation-on-compact-manifolds-ii-non-rigidity-of-euler-flows/

Stupid question
>>10427499

>>10427674
I don't think your argument will work because you're throwing away too much structure. What makes Ramsey-type theorems tick is the regularity of degrees; I cannot recall any theorem (in any part of graph theory) where dumping edges onto a graph arbitrarily accomplished anything.

The only way I know of doing this is slick, but requires you to know a couple of more elementary Ramsey results; you can either prove them, or find something uglier but more basic.

Pick a vertex v, and partition the 33 remaining vertices into subsets R,B,Y based on the colour of the edge to v. Since there is no blue K3 or red K3, R contains no red edges, so it is coloured blue/yellow with no blue triangle. If it has a yellow K4, done. Otherwise (here is the first ramsey result) R(3,4) = 9, so R has <= 8 vertices. Similarly, B <= 8.
This implies Y >= 33-16 = 17, but (here is the second ramsey result) we know R(3,3,3) = 17, so there is a monochromatic triangle in Y. But it's not red or blue so it's yellow, and it's joined to v by all yellow edges, and there's your K4.

>>10417432
/mg/bros I've spent so fucking long trying to find a closed form for some god damned polynomials. The first five are
[math]p_1(x)=2,~p_2(x)=8-2x^2,~p_3(x)=32-12x^2,
~p_4(x)128-64x^2+6x^4,~p_5(x)=512-320x^2+60x^4[/math]
and they have the property that
[math]
p_n(0)=0,~p_n(1)=\binom{2n,n}[/math] for all n.

Does anyone who's better at knowing their special functions than I am have any ideas about what these fucking things could be?

Hermite polynomials nearly work but not quite, and I haven't been able to get the hypergeometric function to work either.
I hate not being able to give explicit closed forms for shit I write.

>>10429119
Can't latex or read right, should be [math]p_n(0)=2^(2n-1),~p_n(1)=\binom{2n,n}[/math]
>>10428017
Well what do you want to get out of analysis? Those books are good for different things
To people who liked Stein and Shakarchi I'd recommend Freitag and Busam which has a great introduction to modular forms.

>>10429129
>p_n(0)=2^(2n-1),~p_n(1)=\binom{2n,n}
[binom(2n,n)-2^(2n-1)]x + 2^(2n-1)

>>10417432
DROP THE FUCKING S IMMEDIATELY

>>10429314
NO

>>10429296
>>p_n(0)=2^(2n-1),~p_n(1)=\binom{2n,n}
also
[binom(2n,n)-2^(2n-1)]x^k + 2^(2n-1) for all k>=1

>>10429296
>>10429334
You might be missing a sum or something there, are you?

>>10429334
You must have missed an index or something up, your ks and ns don't make sense since you'd be describing a polynomial with constant coefficients that way.

>>10429396
>You might be missing a sum or something there, are you?
>>10429415
>You must have missed an index or something up, your ks and ns don't make sense since you'd be describing a polynomial with constant coefficients that way.
The polynomials satisfy p_n(0)=2^(2n-1) and p_n(1)=\binom{2n,n}

>>10429421
anon, you're replying to a post which already has the first few polynomials, it's asking for suggestions for a general form for those, not just any polynomial which satisfies those conditions.
>>10429119
I notice that the coefficients of x^2 are always multiples of 2^(2n-2). They do appear similar to some polynomials of the form f_n(x)/x^n where f_n(x) alternates between odd and even polynomials.

>>10429119
I also notice that the coefficients of x^4 are again multiples of 2^(2n-6), i.e. for n=4 and n=5, 2.3=6, and 4.15=60, which suggests a double factorial, since 15=3.5

What route did you guys take after finishing your undergrad?

>>10429948
janny
>>10429119
see if p_n(x)/x^(n-1) solves a differential equation you know. Too lazy to do this myself though, someone who wants to show off probably could

>>10429957
Nobody really makes it, huh?

>>10429948
Any route was ok, since my studies were simply connected.

>>10428888
Thanks. I was not familiar with R(3,3,3). A very elegant solution.

>>10430318
.

>>10429119
The first three are
[math](\sqrt2x)^nT_n(\sqrt2/x)[/math]
but then you get 4x^4 and 40x^4 instead of 6x^4 and 60x^4.
If I were smarter this would suggest something to me.

>>10430013
So there's no holonomy, either?
>>10429957
It's not showing off if you've already pointed the way.

>>10428607
>you are not educated enough to understand them
It's this.

I find them difficult to understand a lot of the time, and I don't find the exercises very good.
I'm an MSc level student but it's a while since undergrad. What areas would you say I needed to be familiar with to get something from these books?
Should I be working on my Diff Geom?

Has anyone succeded in creating a mathematical function of a plump 3D ass? I tried googling around to find solutions but most of the results seemed very underwhelming. It seems weird to me that this hasn't been really explored before considering how much mathematical talent is out there. SOMEONE has to have both a mathematical and a lewd mind.

I am reading a representation theory book from the 1960s and I am liking it.

Has the field changed much since then? I am enjoying this book but worry it might be archaic

>>10430695

> what is the entire field of computer graphics

>>10430839

I'm a brainlet, please bear with me, I meant like a relatively simple mathematical expression.

>>10430539
>>10429957
Put these together: substitute
[math](\sqrt2x)^nT_n(\sqrt{2/x})[\math]
into the Chebyshev equation, and throw away the terms of the second order derivative.
Then maybe see if there's a fudge factor that works for these polynomials.

>>10430635
>So there's no holonomy, either?
Wtf?

>>10430837
>Has the field changed much since then?
Probably yes. Depends on what objects you're looking at representations of.
The only field of representation theory that has been stagnant enough that a book from the 60s is still current is the basic theory of Lie algebras (the standard reference texts for this are still Bourbaki and Humphreys' shitty little book from the early 70s).
Anything else is going to be very different. The representation theory of algebras has changed so much that books from the 60s are probably borderline useless now (for a handful of examples, homological methods are now used extensively, Hopf algebras were just babies in the 60s and have absolutely exploded since then, quivers are critical now and weren't even defined until the 70s, and you really shouldn't miss quivers because they're the most aesthetic part of representation theory)
Basic theorems on finite groups are probably the same, but stuff is structurally different nowadays because of categorical language and reasoning. Plus, a hell of a lot has happened in group theory since the 1960s.

Can operations like + and - be related to set theory operations? I am trying to prove something is true for all natural numbers without using induction. Could I use the sets and relate union to addition and subtraction to the complement or something? Please don't spoil it just say yes or no.

>>10431237
No.

>>10431247
Fuck

>>10431253
I mean, it's kind of obvious. AUA=A for literally any A, but 1+1=2.

>>10430661
I'd say that, for now, forget about the ODE book, and use the mechanics text to supplement a more rigorous book on differential geometry, such as Lee or Tu, and on classical mechanics. It's definitely ok to struggle with Arnold as an undergrad, just don't rush and use it alongside with a more traditional text.

>>10431298
[math]\mathbb{Z}_1[/math].

>>10429119
These polynomials satisfy the differential equation
[math](a_nx+4x^2)p_n(x)+2\{4(n-1)-(2n-3)x\}p'_n(x)+n(n-1)p_n(x)=0[/math]
where I can't determine the exact form of [math]a_n[/math] because there are only two data points but [math]a_4=-40/3,~a_5=-16[/math]
Does anyone know what type of equation this is? It looks sort of like a hypergeometric equation but I don't know.
Once this equation is identified this basically solves your problem.

>>10432636
That should be [math]x(a_n+4x)p''_n(x)[/math], typo.

>>10418809
I think that's super excessive, bound |int(f(x) - g(x)| < epsilon using triangle inequality for integrals and define g(x) = f(x - c), and you get ez continuity with ed

>>10428755
lang is a meme

>>10432738
stop posting this every thread

>>10432738
Lang is unironically one of the best textbooks I've ever read. His perspective is 10/10

Hello guys, I know this is going to sound retarded to you but I how did I write a proof which shows "for all integers n, if n is odd then n^(2) is odd"

>>10432900
If n^2 is even then it must be a multiple of 4. Otherwise its square root would not be an integer.
If n^2 is a multiple of 4 then n cannot be odd since it is a multiple of 2.

I have a summer ahead of me and I wanna do a crash course on HS math for my college. What topics do you think I should focus on? Im thinking going back to some trigonometry and calculus as it was a bit rushed when I was in HS. Any other thoughts?

>>10432913
thanks man but the teach would mark that wrong, we have to write it out in this weird fancy notation in this class. I really hate it for some reason, I love calculus but this stuff is boring pointless and annoying.

>>10432764
REALLY

does it really matter whether you find eigenvalues and vectors through [math]det(A - tI_n) = 0[/math] or [math]det(tI_n - A) = 0[/math] ?

>>10432928
>but the teach would mark that wrong, we have to write it out in this weird fancy notation in this class
You didn't give this information when you asked the question so how is /mg/ supposed to give you not only the right answer but also in the notation you want?

>>10432934
remember the properties of determinants? The one where you can pull constants out under certain conditions?

>>10432934
No

>>10432934
No one finds eigenvalues that way in the real world

>>10432934
A determinant measures volume. If you're saying a determinant is equal to zero then you're saying a given volume is zero.
Clearly any multiple of that volume will also be zero.

>>10432934
No, but the second one looks nicer because monic polynomials are nice.

>>10432980
right I see.
For some reason I thought the values would be negated, but in retrospect I can not see why I thought that.

LetPbe a polygon in the plane. We first choose a fixeddirection in the plane that is not parallel to any edge ofP.Thisisalways possible becausePhas a finite number of edges. Then any pointxin the plane not on∂Pfalls into one of two sets:1. The ray throughxin the fixed direction crosses∂Pan even numberof times:xis exterior. Here a ray through a vertex is not counted ascrossing∂P.2. The ray throughxin the fixed direction crosses∂Pan odd number oftimes:xis interior.Notice that all points on a line segment that do not intersect∂Pmustlie in the same set. Thus the even sets and the odd sets are connected.And moreover, if there is a path between points in different sets, then this path must intersect∂P.

Im confused, say we have a polygon square and I choose a point inside the square and draw a line through it that isnt parallel to other lines, wouldnt it cross ∂P twice? Thus using the proof it would be considered exterior

>>10422900
ANY metric completion of Q is either Q, R, or some p-adic. So it makes sense to study them.

>>10422900
There are p-adic theories of quantum gravity.
In some sense it makes a lot of sense since they have the property that two balls are either disjoint or one contains the other from the ultrametric inequality, so you can naturally interpret a sub-Planck scale spacetime as being more like an ultrametric spacetime.
I played around with this a few years ago and managed to show that this appears to imply that spacetime cannot have trivial curvature below the Planck scale, even in a Minkowski (large scale) spacetime. I never published this though because I had no idea how to really say anything more meaningful about its implications or whether such a spacetime would even make sense. Causality breaks down at that level, for one.

Anyone here tutor final year highscool students?

>>10418548
You can approximate any function with a step function. Now extend the step function to a continuous function and you're done homie.

>>10422900
A big motivation is to find solutions to equations in the rationals. Obviously if an equation has solutions in the rationals then it has them in the p-adics. A lot of the time the existence of a solution in the p-adics may help to discover a solution in the rationals. For example quadratic forms have solutions in each p-adic (including R) only if they have a solution in the rationals.
Since equations are often easier to solve in the p-adics (Hensel's lemma) this gives new methods of attack.

>>10431401
Thanks. I actually bought the Tu book recently. Can you recommend a classical mechanics text?

>>10433426
Whittaker or Landau and Lifshitz are both about as good as you'll get.
If you want to really challenge yourself then try Abraham and Marsden but this is really far above and beyond.

>>10431237
yes


(hint: x+1 := xu{x})

>>10432900
If n is odd then it has the form n=2m+1 for some integer m.
(2m+1)^2=4m^2+2m+1
Clearly this is odd.

>>10425537
Yo

Hello. I designed a memelist for myself, what does everyone think? (second semester analysis student, took nonrigorous LA/DE/calc sequence then realized I wanted to be a math major but my math abilities are lacking behind my classmates because of this)

phase 1:
>pugh analysis/apostol analysis
>palka complex

phase 2:
>munkres
>hoffman+kunze

phase 3:
>all the stein+shakarchi analysis books
>dummit+foote abstract
>some kind of number theory book

Not really terribly concerned about what comes after that at the moment.

>>10434765
It's all wrong. Start with Linear and Analysis, then go for Complex and Abstract, then Topology and Number Theory. Once you know topology, you can study measure theory, which opens up the path for Fourier analysis.

>>10434814
the problem is I'm in a complex analysis course right now (which was a fucking mistake but it's too late to drop without getting a W and looking like a tard)

>>10434814
Wrong again. Real analysis, then metric / NV spaces ('silly integration and differentiation'), then topology. After that complex analysis, algebra and elementary geometry. Finally real analysis (from measure theory, lebesgue / hardy / berggman spaces, functional analysis, pde and whatever you need whenever you need), complex geometry, algebraic geometry, schemes, number theory, and so on.

Given two natural numbers a and b, 1 < a < b, does there exist a positive real number p other than 1 such that a^p and b^p are natural numbers?

>>10434873
Let p = 2

>>10434864
>implying the theory of metric spaces isn't a part of topology
>completely cutting off linear algebra
>going way beyond the immediate stuff for no reason
Honestly.

>>10434885
>implying the theory of metric spaces isn't a part of topology
It's Functional Analysis.

>>10434885
>>10434864
>>10434814
I took nonrigorous linear and our class taught us all the topology and metric spaces necessary for analysis. Time is finite so I need to get a good grade in complex rather than relearning linear right now. But what is better, hoffman+kunze or axler? axler seems like a fucking meme.

>>10417432
>tfw you just big-dick hand-wave your proofs in your papers because you know all the assertions are correct
>tfw everyone lets it slide because they eventually see its true as well
Non-rigorous intuition master race reporting in

>>10433084
A ray is not a line. A ray has an endpoint, (in this case, x), a line does not. So in your example, the ray crosses the border of the square once.

>>10434873
>>10434882
D'oh

*non-integral real number p

>>10434911

>>10434911
>>10434948
tf is this meme

>>10434899
Axler is fine if you've taken nonrigorous linear. The biggest problem with Axler is that using it exclusively results in students who suck ass at actually computing things, and even if your goal is to be a 100% pure math snob you cannot get away from having to rely on computation with matrices sometimes. If you've already taken a basic course, this isn't an issue.

>>10434951
looks like some family photos to me. Father and son is my guess.

>>10434968
This is some grade-A semitic autism

>>10434959
Thanks, then I'll either use that or just skip the first couple chapters of H+K that are pure computation.

>>10434975

>>10434975
the last page of the bible

>>10434885
>implying the theory of metric spaces isn't a part of topology
Yes. What I mean with metric spaces / nvs is like 'all the norms are 1-Lipschitz', 'all the norms on R^n are equivalent', convergence 'theorems', ..., Banach-Caccioppoli, implicit/local inverse functions, and friends. I would not strictly call that topology.
>completely cutting off linear algebra
Come on.
>going way beyond the immediate stuff for no reason
We were talking about meme lists. You could learn all that in a year (or maybe not).
>>10434899
What do you need linear algebra for? Any book is fine, take the shortest and eat it in few days.
For complex analysis you will need to know at most the definition of linear map. Of course you should know that you can sum / multiply complex numbers (duh), convergence of (power) series, what a derivative is, but in all probability you will see that in the course.

>>10434906
>not leaving the proofs as an exercise to the reader

>>10417432
Any other PhD's here have a foreign language requirement?

>The department expects Ph.D. candidates to be able to read mathematical material in a second
language selected from French, German, or Russian.

Which areas of math are these most useful for?

>>10434916
[math]p=\int^2_0 dx[/math]

>>10435096

>>10435096
Huh, my university's PhD program mentions precisely those three languages — Spanish and English presumed to be already known.

>>10435334
French for algebraic geometry I presume, not sure about the other ones.

>>10435096
>mandatory humanities requirement
which school for brainlets do you go to?

\tilde{H}

I'm looking at this problem in my Hatcher Algebraic Topology Text.

$\tilde{H}_i(S^n-X)\approx \tilde{H}_{n-i-1}(X)$ when $X$ is homeomorphic to a finite connected graph.

Any hints?

>>10435096
Algebra for German, Algebraic Geometry for French, Russian for a lot of stuff desu, no specific area but many famous authors (eg. Manin, Arnold, Gelfand, Drinfel'd...) some of whose papers are not translated/have hard to find translations

I'm looking at a problem in Hatcher's Algebraic Topology. Got any hints?

[math]\tilde{H}_i(S^n-X)\approx \tilde{H}_{n-i-1}(X) [/math] when [math]X[/math] is homeomorphic to a finite connected graph.

Point/set topology is completely destroying me, I have less than 50% right now and a test Friday.
How do I learn this shit? Everything seems to be pulled out of nowhere but flaunted about like it's obvious. My professor just gets upset, but not rude, with how dumb I am, and classmates aren't much help.
We're using munkres topology 2nd edition, but I don't really think that matters.

>>10435451
what are you confused about

What's an algebraic curve

>>10435398
>homeomorphic to a graph
>implying I even know what that means
Did you try using Mayer-Vietoris? I get the impression that you're supposed to naturally produce a division of the space depending on the graph, and then induct on the number of pieces (i.e. what is the graph).

>>10435477
Hmm I didn't think to use Mayer-Vietoris, but I was thinking of using induction. Sorry if I misunderstand, but is there something confusing about the question? I saying this based on the greentext.
I appreciate the help tho. Graphs aren't my strong suit desu

I made some progress. >>10435477
I have that [math] \tilde{H}_{n-i-1}(X) \approx \mathbb{Z}^e [/math] if [math]i=n-2. [/math] and [math]0 [/math] otherwise where [math]e [/math] is the edges in [math]X/T [/math] where [math]T [/math] is the spanning tree of [math]X [/math].

>>10435466
Just all of it, honestly. I still don't get how complements and openness/closedness have any use with each other, or how continuous mapping compact spaces means they're both closed.
I dunno, maybe like a video lecture with animations for my low I brain.

>>10435398
Just note that a finite graph can be embedded in R^3 so just use excision on lower dimensional spheres until you get the S^3 case

>>10435467
A set of elements in affine space defined by a set of polynomial equations (ie a variety) whose only proper subvarieties are points

how can I be the SMARTEST engineer

>>10426853
based yukari poster is not Rapcak, i called his department and he was giving a talk at the time yukari poster was here

>>10435392
>no specific area but many famous authors (eg. Manin, Arnold, Gelfand, Drinfel'd...) some of whose papers are not translated/have hard to find translations
While this is true, it should be kept in mind that two of those guys are dead and the other two are quite old. Russian mathematics nowadays is not nearly as strong as it was in the Soviet era.

>tfw still waiting for 5/6 grad applications to come back

>>10435687
Can't wait for this feel. D-did you apply to PhD programs?

>>10435800
Yeah, they're all PhD programs. At least the one that replied was an acceptance so I'm not completely shitting myself right now, but it wasn't particularly high on my goal list either.

>>10435810
Sick bro, totally cool man. High five. Nice. Proud of you. Excellent. Good job. Keep going.

Hi I know NOTHING about matrices
I missed everything that was covered on it in high school due to being sick and being a high schooler I didn't give enough fucks to cover the material myself. I'm very likely to be touching matrices this semester and much more in depth next semester. What resources would you recommend for someone wanting to get up to speed on the topic?

>>10435451
>>10435539
you sound like you've never taken real analysis
or you're just dumb
either way, you obviously shouldn't be taking topology if you don't understand open/closed sets intuitively. your professor pretends it's obvious because it is.
compactness is a strange concept to people who get the open/closed stuff easily and have taken analysis, so you're not in a good position.

>>10435875
>I missed everything that was covered on it in high school due to being sick
Sick with what?

>>10435810
well that's nice
at least you're sort of set
>>10435875
dude you literally just fucking multiply them and take determinants and that's all you learn about them in high school
some people will never have seen them before assuming you're taking an introductory linear algebra course
calm the fuck down

>>10435880
I would get pretty bad asthma attacks
>>10435885
goodness I hope so

>>10435810
So uh what's the procedure for going from undergrad "straight" to your PhD? Undergrad TA'ing, REUs, asking to take some grad courses, tutoring and gres n shit?

>>10435913
Do a thesis. Get published before graduating if you can.

>>10417432
any of you lads know wtf I'm doing wrong, me on the left the fags over at DAT bootcamp on the right,


aren't we applying the same reasoning here?

>>10436144
>aren't we applying the same reasoning here?
it's the exact same thing
I don't understand what your problem is

>>10432934
yes, the second way will change the sign of the eigenvalues

>>10436146
I don't see the answer on the multiple choices.

>>10435096
is this at berkeley?

>>10436150
oh fuck
nvm
it's simplified
holy shit....
I wasted 4 mins on that shit out of the 45 I'm allotted

>>10435398
apply alexander duality

>>10436147
r-really?
I got a different sign when doing inv(A) vs inv(-A), but is not
(1 - t) and (t-1) the same zero

>>10436147
no, it wont you idiot
>>10436193
stop listening to the child

>>10435565
So you are assuming irreducibility.

>>10435467
There are way too many definitions of this. I don't like >>10435565 's definition because it assumes affine, when usually you care about projective curves.

The usual definition is "variety of dimension 1", where dimension is Krull dimension, i.e. maximum length of a chain of irreducible subsets. The ambiguity comes from what "variety" could mean. It may or may not mean irreducible. It should be finite type (or even just locally finite type) over a field. The field may or may not need to be algebraically closed. It may or may not mean separated. It pretty much always means reduced. It may even mean geometrically reduced/irreducible/integral.

The moral of the story is that there is no one definition and so many authors clarify what they mean at the start. If in doubt, you should just think of one-dimensional irreducible subsets of projective or affine space over an algebraically closed field.

>>10435640
>barely average student
>giving a talk
sure

>>10437295
hush undergrad, PhD students routinely give talks at seminars about their work

>>10433682
Thanks, I tried finding a "formula" for subtraction with sets but I have a feeling it won't be clean. I just handed in a cleaner proof that I had more confidence in. I'll try to figure this out though. Thanks again.

>>10437301
LOL